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#### YEAR 10 FOUNDATION MATHEMATICS – SA1 - ASSIGNMENT – TERM 1, 2023 - PAGE 1 Subject Year 10 Foundation Mathematics Class name Student name Teacher name Task title Draft due date Final due date   Technique Problem solving and modelling task Mode Written: 600-800 words excluding tables, appendices, figures and diagrams Text type Formal mathematical report Duration 3 weeks Task purpose Apply the problem-solving and modelling approach (formulate, solve, evaluate and communicate) to investigate and model a situation to formulate a conclusion

###### Math

YEAR 10 FOUNDATION MATHEMATICS – SA1 - ASSIGNMENT – TERM 1, 2023 - PAGE 1

Subject Year 10 Foundation Mathematics Class name

Student name

Teacher name

Task title Draft due date Final due date

Technique Problem solving and modelling

task Mode Written: 600-800 words excluding tables,

appendices, figures and diagrams

Text type Formal mathematical report Duration 3 weeks

Apply the problem-solving and modelling approach (formulate, solve, evaluate and communicate) to

investigate and model a situation to formulate a conclusion. Solve problems involving the surface area

and volume for a range of prisms, cylinders and composite solids.

Context

Profit depends on many factors; two of the main factors are the cost of the goods being sold and their sale

price. Companies are very keen to obtain maximum profits and so need to be mindful of both factors whilst

still securing the biggest market share.

Any containers holding products need to be eye-catching but also cost efficient. The smaller a container’s

surface area, the fewer the materials that are needed for it to be manufactured and therefore, in general,

the lower its cost of production.

Your task is to determine if it is possible to find the smallest surface area given a specified volume and

three types of containers. You will need to use your knowledge of the surface area and volume of cylinders,

prisms and composite solids to compare the containers and justify your findings.

You need to write a formal mathematical report that demonstrates the following:

• Outlining your plan to determine the dimensions of the containers to achieve the specified volume

and their surface area

• Using trial and error or other method to find the smallest surface area.

• Evaluating the validity of your results and refining, if necessary, to determine whether you have a

suitable strategy and solution

Scaffolding

• You are required to use the problem-solving and modelling approach – see the “Student Guide”

provided for further information.

• Your solution needs to be communicated using a report genre (introduction, body and conclusion) which

can be read independently of this task sheet – see the “Report Template” provided.

YEAR 10 FOUNDATION MATHEMATICS – SA1 - ASSIGNMENT – TERM 1, 2023 - PAGE 2

Stimulus

Below are the three types of containers to be considered. The required volume of each container is

600cm3. No other dimensions have been provided.

Cube

Cylinder

Half cylinder on rectangular prism

Checkpoints

• 5pm Wednesday 22nd February 2023: Students submit their draft to Draft via the QLearn dropbox.

• 5pm Friday 5th March 2023 (Due date): Students submit their final to Final via the QLearn dropbox.

Conditions

• You are permitted to use the BrisbaneSDE Writing Guide.

• You are permitted to access computers, student notes, books and / or learning materials.

• You are permitted to use technology to complete this assignment, including calculators, spreadsheet

and word processing programs such as Word or Excel and the internet for research.

Student declaration

The following declaration must accompany your report:

By submitting this item, I declare that the work submitted:

• is my own work and has not been written by any other person,

• contains no plagiarised material, and has not been obtained from any other source except where due

YEAR 10 FOUNDATION MATHEMATICS – SA1 - ASSIGNMENT – TERM 1, 2023 - PAGE 3

Marking Criteria

Student Name: Teacher Name: UF: PSR: Overall Grade:

A B C D E

Understanding and Fluency

Communicate

Mathematical

language and

symbols

• Accurate use of appropriate technical

vocabulary, procedural vocabulary and

conventions to develop the response.

• Coherent and concise organisation of the

response, appropriate to the genre,

including a suitable introduction, body

and conclusion.

• Use of technical vocabulary, procedural

vocabulary and conventions to develop the

response

• Organisation of the response, including a

suitable introduction, body and

conclusion.

• Use of some appropriate language and

conventions to develop the response

• Adequate organisation of the response –

completion of some parts of the template

• Use of everyday language to develop

a response

• Basic organisation of the response and no

use of template

• Use of everyday language

• Unclear and disjointed organisation of

the response.

Formulate

Conceptual

Understanding

• Accurate translation of all aspects of the

problem by identifying all relevant

mathematical concepts and techniques

• Accurate explanation of two appropriate

and relevant assumptions

• Accurate explanation of two relevant and

appropriate observations

• Accurate translation of all aspects of the

problem by identifying some relevant

mathematical concepts and techniques

• Statement of two appropriate and

relevant assumptions

• Statement of two relevant appropriate

observations

• Translation of some aspects of the

problem by identifying some mathematical

concepts and techniques

• Statement of one relevant assumption

• Statement of one relevant observation

• Translation of some aspects of the

problem or identification of some relevant

mathematical concepts and techniques

• Statement of an assumption

• Statement of an observation

• No translation of any aspect of the

problem or identification of any

mathematical concept or technique

• No assumptions

• No observations

Procedural Fluency • Appropriate, accurate and demonstrated

use of facts, definitions, mathematical

concepts and procedures to reach a valid

conclusion

• Accurately calculates the dimensions,

volume and surface area of three

containers

• Demonstrated use of facts, definitions,

mathematical concepts and procedures to

reach a reasonable conclusion

• Calculates dimensions, volume and

surface area of three containers

• Demonstrated use of facts, definitions,

mathematical concepts and procedures to

make progress towards a conclusion

• Calculates dimensions, volume and

surface area of two containers

• Some use of some facts, definitions,

mathematical concepts and simple

procedures

• Calculates dimensions, volume or surface

area of one container

• No use of any facts, definitions,

mathematical concepts or simple

procedures

• No attempt to calculate any

dimensions, volume or surface area

Problem-Solving and Reasoning

Solve

Problem-solving

approach

• Appropriate, systematic application of the

problem-solving and modelling approach

(formulate, solve, evaluate)

• Application of the problem-solving and

modelling approach (formulate, solve,

evaluate)

• Attempts to methodically formulate, solve

and evaluate

• Some attempt to methodically solve the

problem

• Disjointed attempt to solve the problem

Mathematical

modelling

• Includes accurate formulae for volume

and surface area of all three containers

• Includes accurate formulae for volume

and surface area of two containers

• Includes accurate formulae for volume

and surface area of one container

• Includes formulae for volume or surface

area of any container

• No formulae provided

Evaluate and verify

Reasoning and

justification

• Evaluation of the reasonableness of the

conclusion and result and includes

demonstration of possible refinements

• Correct explanation of two relevant

strengths and limitations of the model

and/or conclusions

• Logical justification of relevant decisions

• Evaluation of the reasonableness of the

conclusion and result and refinements

suggested but not demonstrated

• Statement about two relevant strengths

and limitations of the model and/or

conclusions

• Statements about relevant decisions or

of the conclusion or result

• Statement about two strengths and/or

limitations of the model and/or

conclusions

• Statements about decisions or choices

• No statement about the reasonableness

of the conclusion or result

• Statement about a strength or a limitation

of the model and/or conclusions

• No statement about any decision or

• No conclusion or result included

• No strengths or limitations

• No decisions stated

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